Please start up time is defined here as the time elapsed when average velocity of a fluid rises from rest to within 1% of its steady state value with the sudden imposition of a pressure gradient in a pipe.
Question: All other things being equal, will fluid flow start up times be shorter when the fluid accelerates from rest to a turbulent flow steady state or rather from rest to a laminar flow steady state?
Hello Raymond,
That is an excellent question... one that I do not have an answer to. I suppose that is would be not so difficult to figure out with an experiment. My guess would be laminar flow would take longer.
Best regards,
Gregory Patience
I assume that "all other things being equal" means that the end mean velocity and the applied pressure gradient is the same, so the only change between the two states would be a different viscosity. Since the viscosity for a laminar end state needs to be larger (lower Reynolds number), I would tend to agree with Gregory that the acceleration takes longer in the higher viscosity case.
Thanks Greg and Michael.
I am trying to find out if I can use the laminar flow incomprehensible fluid approximation to start-up times (@Greg: equations 26 and 32 in your paper with Anil K. Mehrotra: "Laminar Start-up flow in Short Pipe Lengths") as an upper bound estimate of start up times in turbulent compressible fluid flow.
Both your answers concur that that could be an analytical upper bound estimate for "Turbulent compressible flow". Now all I need is an answer to my other question posted here, as to whether the acceleration would be faster in a compressible (expansible fluid like air) or slower when a suction pressure is applied? If acceleration is likely the same or faster, then it means I can. If you could both please help me resolve this I would appreciate it a lot. Would the start up likely take longer in an incompressible or compressible fluid, when suction is applied?
for inviscid flow, this question can probably be answered by a 1-D numerical analysis. The difference is that in compressible fluid the density can change and an expansion fan forms at the suction side, while in incompressible fluid all the mass has to be accelerated simultaneously. I would expect that the compressible fluid starts to move faster, but the exit mass flow varies more temporally.
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